2006
DOI: 10.1137/050627538
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Optimal Disturbance Attenuation for Discrete‐Time Switched and Markovian Jump Linear Systems

Abstract: An exact condition for uniform stabilization and disturbance attenuation for switched linear systems is given in the discrete-time domain via the union of an increasing family of linear matrix inequality conditions. Associated with each Markovian jump linear system is a switched linear system, so we obtain a necessary and sufficient condition for almost sure uniform stabilization and disturbance attenuation for Markovian jump linear systems as well. The results lead to semidefinite programming-based controller… Show more

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Cited by 80 publications
(34 citation statements)
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“…This means that the resulting equivalent LPV-SS form contains matrices which not only depend on p k but on its time-shifted version as well. This dynamic-dependence has been encountered and analyzed in LPV control synthesis (Lee and Dullerud (2006)), system theory (Tóth (2010)) and identification (Tóth et al (2009)). Using state transformation with dynamic dependence has also been proved to characterize all equivalent LPV-SS representations of a given LPV system (Tóth et al (2011)).…”
Section: A(p) B(p) C(p) D(p)mentioning
confidence: 99%
“…This means that the resulting equivalent LPV-SS form contains matrices which not only depend on p k but on its time-shifted version as well. This dynamic-dependence has been encountered and analyzed in LPV control synthesis (Lee and Dullerud (2006)), system theory (Tóth (2010)) and identification (Tóth et al (2009)). Using state transformation with dynamic dependence has also been proved to characterize all equivalent LPV-SS representations of a given LPV system (Tóth et al (2011)).…”
Section: A(p) B(p) C(p) D(p)mentioning
confidence: 99%
“…Another body of work which utilizes multiple Lyapunov functions and is of particular interest for us appears in [36], [38], [35], [37]. In these papers, several fundamental control problems (e.g.…”
Section: Contributions and Organizationmentioning
confidence: 99%
“…[32], [13], [15], [36], [38], [35], [37], [30], [29], [20]. Perhaps one of the earliest references is the work on "piecewise quadratic Lyapunov functions" in [32].…”
Section: Contributions and Organizationmentioning
confidence: 99%
“…The parailleters of these systems are indexed, and the indices are called the system 1odes. The papers [72,73] focus on the discrete-time domain, and consider the problems of Il iforil exponential stability atid uniform disturbance attenuation for Markovi;ii jump linear systems. I lere uniiformity refers to almtost sire stability and 2-gain of the sequences of modes, called switcliinig sequelices: tha.t are admissible by the automaton which describes the larkov process.…”
Section: 5mentioning
confidence: 99%